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Equilibrium refinements for the network formation game

Author

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  • Rahmi İlkılıç

    (Universidad de Chile)

  • Hüseyin İkizler

    (Bilkent University and Presidency of the Republic of Turkey Head of Strategy and Budget)

Abstract

This paper examines a normal form game of network formation due to Myerson (Game theory: analysis of conflict, Harvard University Press, Cambridge, 1991). All players simultaneously announce the links they wish to form. A link is created if and only if there is mutual consent for its formation. The empty network is always a Nash equilibrium of this game. We define a refinement of Nash equilibria that we call trial perfect. We show that the set of networks which can be supported by a pure strategy trial perfect equilibrium coincides with the set of pairwise-Nash equilibrium networks, for games with link-responsive payoff functions.

Suggested Citation

  • Rahmi İlkılıç & Hüseyin İkizler, 2019. "Equilibrium refinements for the network formation game," Review of Economic Design, Springer;Society for Economic Design, vol. 23(1), pages 13-25, June.
    • Handle: RePEc:spr:reecde:v:23:y:2019:i:1:d:10.1007_s10058-019-00218-y
    DOI: 10.1007/s10058-019-00218-y
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    References listed on IDEAS

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    1. Antoni Calvó-Armengol & Rahmi İlkılıç, 2009. "Pairwise-stability and Nash equilibria in network formation," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 51-79, March.
    2. Jackson, Matthew O. & van den Nouweland, Anne, 2005. "Strongly stable networks," Games and Economic Behavior, Elsevier, vol. 51(2), pages 420-444, May.
    3. Berno Buechel & Tim Hellmann, 2012. "Under-connected and over-connected networks: the role of externalities in strategic network formation," Review of Economic Design, Springer;Society for Economic Design, vol. 16(1), pages 71-87, March.
    4. Bloch, Francis & Jackson, Matthew O., 2007. "The formation of networks with transfers among players," Journal of Economic Theory, Elsevier, vol. 133(1), pages 83-110, March.
    5. Richard Baron & Jacques Durieu & Hans Haller & Rahul Savani & Philippe Solal, 2008. "Good neighbors are hard to find: computational complexity of network formation," Review of Economic Design, Springer;Society for Economic Design, vol. 12(1), pages 1-19, April.
    6. Christophe Bravard & Sudipta Sarangi & SUMIT JOSHI & AHMED SABER MAHMUD, 2016. "Network Formation under Multiple Sources of Externalities," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 18(2), pages 148-167, April.
    7. Francis Bloch & Matthew Jackson, 2006. "Definitions of equilibrium in network formation games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(3), pages 305-318, October.
    8. Calvo-Armengol, Antoni, 2004. "Job contact networks," Journal of Economic Theory, Elsevier, vol. 115(1), pages 191-206, March.
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    Cited by:

    1. Chenghong Luo & Ana Mauleon & Vincent Vannetelbosch, 2022. "Coalition-proof stable networks," Review of Economic Design, Springer;Society for Economic Design, vol. 26(2), pages 185-209, June.
    2. Gallo, Andrea & Meroni, Claudia, 2021. "Towards a solution concept for network formation games," Economics Letters, Elsevier, vol. 198(C).

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    More about this item

    Keywords

    Networks; Network formation; Pairwise-stability; Equilibrium refinement;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • L14 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Transactional Relationships; Contracts and Reputation

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